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With numerous and ambiguous sets of information and often conflicting requirements, construction management is a complex process involving much uncertainty. Decision makers may be challenged with satisfying multiple criteria using vague information. Fuzzy multi-criteria decision-making (FMCDM) provides an innovative approach for addressing complex problems featuring diverse decision makers’ interests, conflicting objectives and numerous but uncertain bits of information. FMCDM has therefore been widely applied in construction management. With the increase in information complexity, extensions of fuzzy set (FS) theory have been generated and adopted to improve its capacity to address this complexity. Examples include hesitant FSs (HFSs), intuitionistic FSs (IFSs) and type-2 FSs (T2FSs). This chapter introduces commonly used FMCDM methods, examines their applications in construction management and discusses trends in future research and application. The chapter first introduces the MCDM process as well as FS theory and its three main extensions, namely, HFSs, IFSs and T2FSs. The chapter then explores the linkage between FS theory and its extensions and MCDM approaches. In total, 17 FMCDM methods are reviewed and two FMCDM methods (i.e. T2FS-TOPSIS and T2FS-PROMETHEE) are further improved based on the literature. These 19 FMCDM methods with their corresponding applications in construction management are discussed in a systematic manner. This review and development of FS theory and its extensions should help both researchers and practitioners better understand and handle information uncertainty in complex decision problems.

Construction is a highly dynamic environment with numerous interacting factors that affect construction processes and decisions. Uncertainty is inherent in most aspects of construction engineering and management, and traditionally, it has been treated as a random phenomenon. However, there are many types of uncertainty that are not naturally modelled by probability theory, such as subjectivity, ambiguity and vagueness. Fuzzy logic provides an approach for handling such uncertainties. However, fuzzy logic alone has some limitations, including its inability to learn from data and its extensive reliance on expert knowledge. To address these limitations, fuzzy logic has been combined with other techniques to create fuzzy hybrid techniques, which have helped solve complex problems in construction. In this chapter, a background on fuzzy logic in the context of construction engineering and management applications is presented. The chapter provides an introduction to uncertainty in construction and illustrates how fuzzy logic can improve construction modelling and decision-making. The role of fuzzy logic in representing uncertainty is contrasted with that of probability theory. Introductory material is presented on key definitions, properties and methods of fuzzy logic, including the definition and representation of fuzzy sets and membership functions, basic operations on fuzzy sets, fuzzy relations and compositions, defuzzification methods, entropy for fuzzy sets, fuzzy numbers, methods for the specification of membership functions and fuzzy rule-based systems. Finally, a discussion on the need for fuzzy hybrid modelling in construction applications is presented, and future research directions are proposed.

The purpose of this paper is to develop a multi-criterion group decision-making (MCGDM) method by combining the regret theory and the Choquet integral under 2-tuple linguistic environment and apply the proposed method to deal with the supplier selection problem.

When making a decision, the decision-maker is more willing to choose the alternative(s) which is preferred by the experts so as to avoid the regret. At the same time, the correlative relationships among the criterion set can be sufficiently described by the fuzzy measures, later the evaluations of a group of criteria can be aggregated by means of the Choquet integral. Hence, the authors cope with the MCGDM problems by combining the regret theory and the Choquet integral, where the fuzzy measures of criteria are partly known or completely unknown and the evaluations are expressed by 2-tuples. The vertical and the horizontal regret-rejoice functions are defined at first. Then, a model aiming to determine the missing fuzzy measures is constructed. Based on which, an MCGDM method is proposed. The proposed method is applied to tackle a practical decision-making problem to verify its feasibility and the effectiveness.

The vertical and the horizontal regret-rejoice functions are defined. The relationships of the fuzzy measures are expressed by the sets. A model is built for determining the fuzzy measures. Based on which, an MCGDM method is proposed. The results show that the proposed method can solve the MCGDM problems within the context of 2-tuple, where the decision-maker avoids the regret and the criteria are correlative.

The paper proposes an MCGDM method by combining the regret theory and the Choquet integral, which is suitable for dealing with a variety of decision-making problems.

The purpose of this paper is to present a new method for evaluation of emergency plans for unconventional emergency events by using the soft fuzzy rough set theory and methodology.

In response to the problems of insufficient risk identification, incomplete and inaccurate data and different preference of decision makers, a new model for emergency plan evaluation is established by combining soft set theory with classical fuzzy rough set theory. Moreover, by combining the TOPSIS method with soft fuzzy rough set theory, the score value of the soft fuzzy lower and upper approximation is defined for the optimal object and the worst object. Finally, emergency plans are comprehensively evaluated according to the soft close degree of the soft fuzzy rough set theory.

This paper presents a new perspective on emergency management decision making in unconventional emergency events. Also, the paper provides an effective model for evaluating emergency plans for unconventional events.

The paper contributes to decision making in emergency management of unconventional emergency events. The model is useful for dealing with decision making with uncertain information.

This paper presents a comprehensive review of the available literature on applications of the rough set theory. Concepts of the rough set theory are discussed for approximation, dependence and reduction of attributes, decision tables and decision rules. The applications of rough sets are discussed in pattern recognition, information processing, business and finance, industry, environment engineering, medical diagnosis and medical data analysis, system fault diagnosis and monitoring and intelligent control systems. Development trends and future efforts are outlined. An extensive list of references is also provided to encourage interested readers to pursue further investigations.

This study aims to improve the reliability of emergency safety barriers by using the subjective safety analysis based on evidential reasoning theory in order to develop on a framework for optimizing the reliability of emergency safety barriers.

The emergency event tree analysis is combined with an interval type-2 fuzzy-set and analytic hierarchy process (AHP) method. In order to the quantitative data is not available, this study based on interval type2 fuzzy set theory, trapezoidal fuzzy numbers describe the expert's imprecise uncertainty about the fuzzy failure probability of emergency safety barriers related to the liquefied petroleum gas storage prevent. Fuzzy fault tree analysis and fuzzy ordered weighted average aggregation are used to address uncertainties in emergency safety barrier reliability assessment. In addition, a critical analysis and some corrective actions are suggested to identify weak points in emergency safety barriers. Therefore, a framework decisions are proposed to optimize and improve safety barrier reliability. Decision-making in this framework uses evidential reasoning theory to identify corrective actions that can optimize reliability based on subjective safety analysis.

A real case study of a liquefied petroleum gas storage in Algeria is presented to demonstrate the effectiveness of the proposed methodology. The results show that the proposed methodology provides the possibility to evaluate the values of the fuzzy failure probability of emergency safety barriers. In addition, the fuzzy failure probabilities using the fuzzy type-2 AHP method are the most reliable and accurate. As a result, the improved fault tree analysis can estimate uncertain expert opinion weights, identify and evaluate failure probability values for critical basic event. Therefore, suggestions for corrective measures to reduce the failure probability of the fire-fighting system are provided. The obtained results show that of the ten proposed corrective actions, the corrective action “use of periodic maintenance tests” prioritizes reliability, optimization and improvement of safety procedures.

This study helps to determine the safest and most reliable corrective measures to improve the reliability of safety barriers. In addition, it also helps to protect people inside and outside the company from all kinds of major industrial accidents. Among the limitations of this study is that the cost of corrective actions is not taken into account.

Our contribution is to propose an integrated approach that uses interval type-2 fuzzy sets and AHP method and emergency event tree analysis to handle uncertainty in the failure probability assessment of emergency safety barriers. In addition, the integration of fault tree analysis and fuzzy ordered averaging aggregation helps to improve the reliability of the fire-fighting system and optimize the corrective actions that can improve the safety practices in liquefied petroleum gas storage tanks.

With respect to multiple attribute group decision-making (MAGDM) in which the assessment values of alternatives are denoted by normal discrete fuzzy variables (NDFVs) and the weight information of attributes is incompletely known, this paper aims to develop a novel fuzzy stochastic MAGDM method based on credibility theory and fuzzy stochastic dominance, and then applies the proposed method for selecting the most desirable investment alternative under uncertain environment.

First, by aggregating the membership degrees of an alternative to a scale provided by all decision-makers into a triangular fuzzy number, the credibility degree and expect the value of a triangular fuzzy number are calculated to construct the group fuzzy stochastic decision matrix. Second, based on determining the credibility distribution functions of NDFVs, the fuzzy stochastic dominance relations between alternatives on each attribute are obtained and the fuzzy stochastic dominance degree matrices are constructed by calculating the dominance degrees that one alternative dominates another on each attribute. Subsequently, calculating the overall fuzzy stochastic dominance degrees of an alternative on each attribute, a single objective non-linear optimization model is established to determine the weights of attributes by maximizing the relative closeness coefficients of all alternatives to positive ideal solution. If the information about attribute weights is completely unknown, the idea of maximizing deviation is used to determine the weights of attributes. Finally, the ranking order of alternatives is determined according to the descending order of corresponding relative closeness coefficients and the best alternative is determined.

This paper proposes a novel fuzzy stochastic MAGDM method based on credibility theory and fuzzy stochastic dominance, and a case study of investment alternative selection problem is provided to illustrate the applicability and sensitivity of the proposed method and its effectiveness is demonstrated by comparison analysis with the proposed method with the existing fuzzy stochastic MAGDM method. The result shows that the proposed method is useful to solve the MAGDM problems in which the assessment values of alternatives are denoted by NDFVs and the weight information of attributes is incompletely known.

The contributions of this paper are that to describe the dominance relations between fuzzy variables reasonably and quantitatively, the fuzzy stochastic dominance relations between any two fuzzy variables are redefined and the concept of fuzzy stochastic dominance degree is proposed to measure the dominance degree that one fuzzy variable dominate another; Based on credibility theory and fuzzy stochastic dominance, a novel fuzzy stochastic MAGDM method is proposed to solve MAGDM problems in which the assessment values of alternatives are denoted by NDFVs and the weight information of attributes is incompletely known. The proposed method has a clear logic, which not only can enrich and develop the theories and methods of MAGDM but also provides decision-makers a novel method for solving fuzzy stochastic MAGDM problems.

The purpose of this paper is to present a newly developed fuzzy-set based model for estimating, allocating, depleting, and managing contingency fund over the life cycle of construction projects.

Fuzzy set theory is utilized in the design and development of proposed contingency modelling framework to incorporate uncertainties associated with the development phases of construction projects. A set of developed indices, measures, and ratios are introduced to quantify and characterize these uncertainties. The developed framework is designed to incorporate expert opinion and provide user-system interaction.

The results obtained from the application of the developed framework on actual project case not only illustrate its accuracy, but also demonstrate its capabilities for contingency management over life cycle of construction projects. Unlike other methods, the framework provides project managers with structured method for contingency depletion utilizing a set of depletion curves and selection factors.

The novelty of the developed framework lies not only in its new developments for contingency estimating but also its modelling for contingency allocation and depletion. It is expected to be of direct value to industry professionals and academics interested in contingency management over the entire life cycle of construction projects. The proposed framework provides management functions and features beyond those generated through Monte Carlo simulation and even those developed using fuzzy set theory.

Contractor prequalification is a typical multiple criteria decision‐making problem that includes both quantitative and qualitative criteria. The conditions surrounding the prequalification decision are often imprecise, subjective and uncertain; assessments are consequently made using linguistic approximations. Fuzzy set theory is specifically designed to handle qualitative and linguistic data based on approximations and provides a method of representing in numerical form the linguistic approximations used to describe the decision‐maker judgments. However, fuzzy set theory has a weakness in identification of the relative weights of the decision criteria. On the other hand, one of the most accurate and easy methods for identifying the relative weights is the analytic hierarchy process (AHP). This paper seeks to address these issues.

The main objective of this paper is to develop a new integrated decision model composed of fuzzy set theory and analytic hierarchy process (AHP) methodologies approach that takes full advantages of the fuzzy set theory and the AHP. Two fuzzy approaches are considered, namely Chang's extent analysis and Jaskowski aggregated group decision analysis.

Both approaches are applied and validated on actual contractors in the Egyptian construction market. A software tool is developed to automate the calculations and a case study is provided.

This research produced a new integrated decision model composed of fuzzy‐AHP methodology approach that takes full advantages of the fuzzy set theory and AHP for tackling the uncertainty and imprecision of contractor prequalification during the prequalification stage, where the decision‐makers comparison judgments are represented as fuzzy triangular numbers. The default criteria used in this model had been collected through the literature review and experts’ opinion for building projects.

In this paper, we present a brief study on various paradigms to tackle complexity or in other words manage uncertainty in the context of understanding science, society and nature. Fuzzy real numbers, fuzzy logic, possibility theory, probability theory, Dempster‐Shafer theory, artificial neural nets, neuro‐fuzzy, fractals and multifractals, etc. are some of the paradigms to help us to understand complex systems. We present a very detailed discussion on the mathematical theory of fuzzy dynamical system (FDS), which is the most fundamental theory from the point of view of evolution of any fuzzy system. We have made considerable extension of FDS in this paper, which has great practical value in studying some of the very complex systems in society and nature. The theories of fuzzy controllers, fuzzy pattern recognition and fuzzy computer vision are but some of the most prominent subclasses of FDS. We enunciate the concept of fuzzy differential inclusion (not equation) and fuzzy attractor. We attempt to present this theoretical framework to give an interpretation of cyclogenesis in atmospheric cybernetics as a case study. We also have presented a Dempster‐Shafer's evidence theoretic analysis and a classical probability theoretic analysis (from general system theoretic outlook) of carcinogenesis as other interesting case studies of bio‐cybernetics.